


Influence

by Bitenomnom



Series: Mathematical Proof [29]
Category: Sherlock (TV)
Genre: Alternate Universe, Gen, Johnlock goggles optional, M/M, Mathematics, The Great Game, alternate first meeting
Language: English
Status: Completed
Published: 2012-10-30
Updated: 2012-10-30
Packaged: 2017-11-17 08:56:12
Rating: Not Rated
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 2,829
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/549815
Author URL: https://archiveofourown.org/users/Bitenomnom/pseuds/Bitenomnom
Summary: <blockquote class="userstuff">
              <p>John’s trip to London did not begin as he had been hoping.</p><p>For one thing, he'd been kidnapped and rigged with explosives.</p><p>Continuation of <a href="http://archiveofourown.org/works/545617">Leverage</a>.</p>
            </blockquote>





	Influence

**Author's Note:**

> Continuation of [Leverage](http://archiveofourown.org/works/545617)! Johnlock goggles optional. The math isn't terribly intense here, but mostly because it's essentially the same math as in the first part. It's just a continuation of Sherlock being the outlier that pulls the trajectory of John's life in a different direction. =D
> 
> Was thinking of doing more in this one, but the truth is I'm also trying to work on a bit of a Halloween special to post hopefully sometime in the next day or so, so right after I post this, I'm off to work on that. [Here's a preview](http://toasterfish.tumblr.com/post/34557467073/come-down-to-lake-pontchartrain-rest-your-soul) of what it entails.

One way of measuring influence is hat values (see [Leverage](http://archiveofourown.org/works/545617)). Hat values are a common measure of the amount of leverage a point has in a regression. The bigger the hat value, the more leverage it has. This value is formed using the “hat matrix,” which is a matrix used to describe how one would transform the actual data values to the predicted values on the line (imagine you are finding a series of equations that will move each individual point, which may or may not be on the line, exactly onto the line). Basically, you are writing the predicted value in terms of the observed values. The hat values are essentially a measure of how much the equation changes if you remove a particular variable—they measure the leverage.

 

The other factor for finding the influence is discrepancy, or how poorly a data point fits the pattern. The residuals can be used to help gauge this. Therefore, in order to get a good measure of influence, which depends on both leverage and discrepancy, one must come up with an equation that involves both factors. One of such equations is known as “Cook’s D” or “Cook’s distance,” and involves multiplying the residuals (errors) by a term related to the hat values. By looking at a plot such as a bubble plot, which measures leverage on one axis and discrepancy on the other with the area of the “bubbles” proportional to Cook’s D, one can easily see which variables might have the greatest influence over the model.

 

 

***  


            John’s trip to London did not begin as he had been hoping.

            Neither did his trip from Brighton, really.

            Lucy was a mess when he finally told her. “We should just be glad I didn’t realize this later,” he tried to say without really much specifying _this_ , which by his reckoning was something along the lines of _that I’m a bloody wreck and apparently can’t get by with a normal life now that I’m back_. How does one tell a perfectly lovely woman who’s been waiting years to marry him that she’s too lovely, too perfect, too well-adjusted? How does one tell such a woman that he only found this out because some crazy bloke staking out in a changing room to try to solve a murder case who later broke into one’s flat had pointed it out to him?

            She was a mess—and rightfully so. John was tempted, _so_ tempted to apologize and crawl back into her arms and comfort her, but by the time his will had broken down enough for him to consider it, she was far beyond that point. She was stuffing his things into the suitcase he’d only barely begun unpacking since his arrival less than a month ago. “I got by fine without you before,” she was saying, “and I’ll do it again, you selfish bastard.”

            “I know,” John muttered. “You’ll find someone better.” Better for her, anyway, definitely.

            John didn’t have much of a choice when he left. He could find an inn, but he scarcely had the funds. And certainly, certainly he couldn’t _stay_ in Brighton—not with the thought of what he’d just done there to haunt him, not when he could go the grocery and bump into Lucy’s father and god, oh god, that was a fight he did not want to begin. He probably wouldn’t lose, but that wasn’t the point.

            And anyway, he’d had nothing in Brighton but Lucy to start with.

            So he would go to London, and probably show up at Sherlock’s door looking like a downtrodden mutt, and hopefully Sherlock would let him stay until he could sort out some work and get a place of his own.

            _Sherlock_ —this wasn’t about him, John thought. Not specifically. Maybe the guy had been the one to be able to just _look_ at John and know all those things; maybe he had awed John as no one had since he’d gotten back from Afghanistan, as it appeared no one could off of the battlefield. It seemed a bit like Sherlock carried a portable battlefield along with him wherever he went—stakeouts, break-ins. Maybe John could help him with this—whatever he was doing. As payment for letting him stay at his flat. But beyond that, John planned to deal with it in stages: leave Lucy first, decide what else is going on later. He couldn’t think about Sherlock _while_ leaving Lucy; that would be like leaving Lucy _for_ Sherlock, even if it wasn’t like that at all.

            When John’s train arrived in London, he stopped to get a bite—no point turning up at Sherlock’s and then eating all his food. The restaurant was quiet, the midnight hour nearing, and John tried to think about anything other than poor Lucy and what a complete arse he’d been to her.

            Of course, that was when his day went downhill for the second time. Well: depending on one’s definition of _downhill_.

            “Sir,” a man at the table behind him said, and John turned around to glance at him and was met with the digging of the barrel of a gun at his shoulder. “You’d better follow me outside.”

            John had his own gun on him, of course, but this was no place to cause a scene. “Right,” he said, and nodded, and stood and hobbled out behind him. When they got outside, he growled, “What’s all this, then?”

            “Get in the car,” he said, stepping over to one and swinging the back seat door open. “My boss wants to see you. Oh,” he reached into the front seat for something, “and put on this coat. Careful, though; it’s rigged with explosives.” He threw it to John and as John caught it, a laser sight appeared on its front.

            _Shit_.

           

 

 

            Sherlock gave in for half a moment and buried his face in his hands.

            Maybe Moriarty somehow knew of Sherlock’s gap in knowledge when it came to space—maybe he had chosen this case deliberately for that reason. Either way, the thought that what had been wrong with the painting would be the _stars_ occurred to him too late, and the little boy was dead. Two of the four puzzles had ended in death—true, the old woman wasn’t his fault, but—well. That wasn’t what mattered. Solving the next puzzle, the last puzzle, was what was important. But there wasn’t a last puzzle, yet. Sherlock dug through his mind for something, anything—was he supposed to have guessed it himself?

            His phone rang.

            Sherlock snatched it up more quickly than ought to have been humanly possible. “Hello?” he answered quietly, evenly, determined not to betray any of his anxiousness.

            “Hello, Sherlock,” said a stiff voice—a familiar voice.

            John Watson’s voice.

            “ _John._ ”

            “Yes,” John said, still in monotone, wooden, “I thought you might say something like that.” A slow breath, forcibly even. “I’m sure you heard me when I said you’d better be careful.”

            “So you brought me back from Brighton only to send me there again,” Sherlock said, trying to swallow down various other things that came to mind, _Are you alright, John?_ or _Where are you?_ or _How did he get you?_ And it was all stupid—all of it: because he couldn’t say such things, and because this was a man he’d met only days ago, for only a brief period of time, yet who was so _interesting_ that he invited him to become his bloody _flatmate_. He would be perfect—Sherlock had known that. He shivered when he thought about how he had been so _wrong_ about John, and then so very _right_ , so right that it shook John down to his core and Sherlock had seen it happen. Many people heard Sherlock’s deductions; John listened. John was strange enough to shift from a drug addict to an adrenaline-junkie army doctor by virtue of mere tan lines.

            “Oh,” John said, “no. Not to Brighton. Johnny here just arrived in London.”

            Oh.

            _God_.

            He’d probably been kidnapped on his way to Baker Street—Sherlock hoped, anyway, and at the same time dreaded, because _John was visiting_ but now John, doubtless wrapped in enough semtex to destroy an entire building, was acting as Moriarty’s voice, and it was Sherlock’s fault.

            _The past two had died._

            “You’d better not let him die,” John said, “like that little boy earlier. Give me something worth my while, and maybe I’ll let him go. You have half an hour to meet me where poor Carl passed away.”

            And he hung up.

            Something worthwhile, something—what was he getting at? It _had_ to be something specific, maybe—oh.

            The files Mycroft had left on his desk, some adorably obvious little thing. Sherlock still had the Bruce-Partington plans, had been putting off giving them to Mycroft for as long as he could. _That_ , surely, was worth something to Moriarty, whoever he was.

            Sherlock put the flash drive in his pocket and swung his coat on before dashing outside to hail a cab. He felt sick—worse, he felt guilty.

 

 

 

            When Sherlock arrived, he entered the pool briskly, or as briskly as he could while still appearing casual. “Is this what you wanted?” he called out, holding the flash drive up. “Just a little something I had lying around the flat. Some sort of _missile_ thing.”

            “I’m disappointed,” came John’s quiet voice as he stepped from the changing stalls. Sherlock’s teeth clicked when he shut his mouth after it dropped open at the sight of John, bundled up in bombs, steady eyes piercing into Sherlock. At that moment, Sherlock thought, they were simultaneously two things: perpetrator and victim; veteran and novice. They were, too, he thought, perhaps, _friends_ , in that moment, but that was likely hoping too much; and if they were, it was most likely Stockholm syndrome on John’s part. Whatever they were, it paused Sherlock’s heart for a moment; when John spoke, he quivered almost invisibly. Was John—did he—or was he still—

            “You should have expected this,” John said. “You should have come more prepared.”

            Sherlock could not muster any words—nothing he wanted to say that he could bear for Moriarty to hear; nothing he wanted to say that he could bear for John to hear.

            “Or did you really think,” John continued, his breathing growing heavier, his eyes now avoiding Sherlock’s, “those silly missile plans…are…worth…John’s…life.”

            And what was he meant to say to that?

            John’s eyes rose to Sherlock, then, meeting him with a drilling stare, a resigned stare, a _he’s probably right_ or maybe _just get it over with, already_ stare.

            “Where are you?” Sherlock finally barked out.

            “Oh, fine,” out strode a familiar man in finely tailored clothing. “Spoil it, why don’t you.”

            Sherlock’s eyes widened.

            “Oh, yes, don’t you recognize me? _Jim from IT._ Jim Moriarty—it’s a _pleasure_ to meet you. Well—again.”

            “What do you want?” Sherlock hissed through his teeth. What else could he possibly have to give to him that would be worth John’s life?

            “Nothing at all, really,” _Jim_ casually strolled closer. “I just thought I’d come by and ask you kindly to stay out of my way. I’m really rather busy, dear, and you’re making things difficult.”

            “ _Please, Jim, will you fix it for me…_ ” Sherlock muttered to himself. “You’re a consulting criminal.” He couldn’t help the swelling in his chest at the thought. _Him_ , another him, on the other side of the coin. “Brilliant.”

            “Isn’t it just?” he smiled, beamed, grinned a reptilian grin. “Of course the problem at hand is just this: I’ve brought John to trade, but I don’t think those missile plans are worth nearly as much to me as he is to you.”

            Sherlock watched John’s eyebrows twitch, struggle not to rise in shock.

            Moriarty tutted. “Not much I can do about that, really, unless you have something better to offer.”

            John tilted his head slightly to one side, a dismissal, nearly a scream of _no_ in the quiet of the pool, because he could probably watch Sherlock’s mind processing dangerous thoughts. It was unnecessary—of _course_ Sherlock wasn’t going to just let Jim kill him so that John could survive.

            “I think you misjudge the situation,” Sherlock said instead.

            “Oh?”

            “You see, John and I have just met.”

            Moriarty stuffed his hands in his pockets, chuckled. “Oh, Sherlock, you aren’t really trying to use _that_ one on me, are you? I’m not an _idiot_. I’ve been watching you for a while, you know. I can tell when you _care_.” He shook his head. “It’s _adorable_.” His grin fell off; his face dropped to seriousness. “It doesn’t suit you, Sherlock. You look like a shark trying to carry a kitten in its mouth. You’re going to bite down one day, and you’re going to _like_ it.” Jim’s grin spread back onto his face and he _was_ a shark, just then, and Sherlock didn’t have to wonder if he spoke from experience. “Let’s save the trouble and do it now.”

            “I don’t think so,” Sherlock said, his voice bubbling from his throat with conviction and confidence. “You came here to get me out of your way.” He strode a wide arc from the edge of the pool inward, and it brought him closer to John. “Do you really think this will help?” He paused; Jim waited, watched. “I _said_ John and I have only just met.”

            “Do stop being repetitive; get to the point.”

            “You’ve had scarcely any time to see us interact.” Sherlock looked to John, eyes scouring up and down, and John stood silent—not that he had much of a choice. He inclined his head slightly. “How do you know he’s not a distraction?”

            “Oh,” Jim said, “ _Oh._ I see.”

            “Kill John, and I have nothing but time to get in your way. In fact, I’ll probably double my efforts.”

            Moriarty laughed. “If you continue getting in my way we _will_ have another problem, whether John survives today or not. I’m still going to kill you, Sherlock, even if I don’t do it right now.” He turned on his toes, nearly humming. “But this _is_ lovely, isn’t it? Yes, I think that can be arranged. You can have a little more fun. You _do_ need it, don’t you, you poor thing.” He turned around and headed back the way he came, speaking as he did so. “But don’t fool yourself _too_ much, Sherlock. I’m not going away. We’re not done, yet.”

            “Of course not.”

            And Moriarty left.

            John nearly collapsed against the wall. “ _Christ_ ,” he breathed. Sherlock yanked the coat from around John’s shoulders and slid it across the room. In each hand he gripped one of Sherlock’s shoulders.

            “Are you all right?”

            “He took my gun,” was all John could think to say, his voice an octave higher than Sherlock had remembered it.

            “Is that all you brought with you?”

            “Only thing that mattered,” John said. Sherlock blinked in surprise—surely someone as attached to his service as John would have— _oh_. Sherlock shifted the collar of John’s jumper slightly in the guise of checking for more bombs; he _was_ wearing his dogtags. John sighed and then, for what seemed like the first time in the entire evening, _really_ looked at Sherlock, _really_ spoke to him. “What did you mean? By my being a distraction?”

            “Not important,” Sherlock breathed, deciding that he did want to actually check John’s jumper for bombs, after all. He added, “I generally live alone. Having a flatmate will doubtless consume a portion of attention I could be spending on other things.”

            “I don’t think that’s what you meant,” John said slowly, evenly.

            Sherlock averted his eyes.

            “You barely know me.”

            “I know plenty. I don’t need to know what flavor of biscuits someone likes before they can become my flatmate.”

            “I meant…”

            “For that, either.”

            It was a fair point. It was also decidedly _not_ normal. “So you think I’d want to live with you, do you?”

            “I play the violin at hours that most people don’t know exist and occasionally store fingers in the refrigerator. Generally that’s enough to stop most people, but I _think_ ,” Sherlock narrowed his eyes, as if making one last calculation, “that’s just enough to _interest_ you.”

            John grinned, though his lips still twitched with nerves. “You may be right.” When his expression shrunk back to something more neutral, he said, “You should know that I’m not—er. Well. Before, you made it sound like you and I were going to be…”

            Sherlock waved his hand dismissively. John couldn’t decide whether he meant to indicate with the gesture that what he had said before was meaningless, or no longer important, or whether what he really meant was _hush, you’ll come around_. The first two seemed more likely; but nothing about Sherlock was likely.

            “So,” John cleared his throat. “Uh, hello. I’m…well. I’m here.”

            Sherlock beamed. “Welcome to London.”


End file.
